Humza Yousaf’s in-laws have been granted permission to leave Gaza, according to a list published by the Palestinian Border Authority.
Elizabeth and Maged El-Nakla, from Dundee, have been named among 92 British nationals who will be permitted to pass through the Rafah border crossing into Egypt.
The couple travelled to Gaza to visit family prior to the conflict erupting and have been trapped there since.
Mr Yousaf’s wife, Nadia El-Nakla, has reported her parents were without clean drinking water and faced "rapidly diminishing supplies".
On Wednesday, the First Minister welcomed the opening of the Rafah crossing which allowed people to leave Gaza, but at the time his in-laws were not among those permitted to do so.
The list published overnight by the Palestinian Border Authority said those named on it must be "present at 7am in the outdoor halls of the crossing to facilitate their travel".
Around 200 Britons in Gaza have so far registered with the authorities, and along with their dependents the total number the UK is trying to secure passage for is thought to be in the low hundreds.
The news will be a relief for Mr Yousaf, who just days ago told how the couple had run out of clean drinking water.
The Scottish FM was able to speak to Ms El-Nakla’s parents on Sunday, posting on X that he feared for their safety.
The Foreign Office said on Thursday that more UK nationals were able to make it into Egypt after two UK aid workers managed to flee Gaza a day earlier, but declined to say how many.
More than 9,000 people have been killed in the Gaza Strip since October 7 when Israel launched its military response to the atrocities committed by Hamas.
Aid agencies are battling a humanitarian crisis in the war-ravaged territory with limited resources, amid calls for the Government to increase their efforts.
It is understood Foreign Secretary James Cleverly spoke to Ayman Safadi, minister of foreign affairs in Jordan, and UAE foreign minister Abdullah bin Zayed Al Nahyan on Thursday about the humanitarian situation in Gaza.
He also spoke to Israel’s minister of strategic affairs, Ron Dermer, about ensuring British nationals are able to cross safely as soon as possible into Egypt, while reiterating the UK’s solidarity with Israel and its commitment to finding a two-state solution.
